README.md

PEPSKit.jl

Tools for working with projected entangled-pair states

It contracts, it optimizes, it may break.

Installation

The package can be installed through the Julia general registry, via the package manager:

pkg> add PEPSKit

Quickstart

After following the installation process, it should now be possible to load the packages and start simulating. For example, in order to obtain the groundstate of the 2D Heisenberg model, we can use the following code:

using TensorKit, PEPSKit, KrylovKit, OptimKit

# constructing the Hamiltonian:
Jx, Jy, Jz = (-1, 1, -1) # sublattice rotation to obtain single-site unit cell
physical_space = ComplexSpace(2)
T = ComplexF64
σx = TensorMap(T[0 1; 1 0], physical_space, physical_space)
σy = TensorMap(T[0 im; -im 0], physical_space, physical_space)
σz = TensorMap(T[1 0; 0 -1], physical_space, physical_space)
H = (Jx * σx ⊗ σx) + (Jy * σy ⊗ σy) + (Jz * σz ⊗ σz)
Heisenberg_hamiltonian = NLocalOperator{NearestNeighbor}(H / 4)

# configuring the parameters
D = 2
chi = 20
ctm_alg = CTMRG(; trscheme = truncdim(chi), tol=1e-20, miniter=4, maxiter=100, verbosity=1)
opt_alg = PEPSOptimize(;
    boundary_alg=ctm_alg,
    optimizer=LBFGS(4; maxiter=100, gradtol=1e-4, verbosity=2),
    gradient_alg=GMRES(; tol=1e-6, maxiter=100),
    reuse_env=true,
    verbosity=2,
)

# ground state search
state = InfinitePEPS(2, D)
ctm = leading_boundary(CTMRGEnv(state; Venv=ComplexSpace(chi)), state, ctm_alg)
result = fixedpoint(state, Heisenberg_hamiltonian, opt_alg, ctm)

@show result.E # -0.6625...